(4x+7)x(7x+4)=

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Solution for (4x+7)x(7x+4)= equation: 


Simplifying
(4x + 7) * x(7x + 4) = 0

Reorder the terms:
(7 + 4x) * x(7x + 4) = 0

Reorder the terms:
(7 + 4x) * x(4 + 7x) = 0

Reorder the terms for easier multiplication:
x(7 + 4x)(4 + 7x) = 0

Multiply (7 + 4x) * (4 + 7x)
x(7(4 + 7x) + 4x * (4 + 7x)) = 0
x((4 * 7 + 7x * 7) + 4x * (4 + 7x)) = 0
x((28 + 49x) + 4x * (4 + 7x)) = 0
x(28 + 49x + (4 * 4x + 7x * 4x)) = 0
x(28 + 49x + (16x + 28x2)) = 0

Combine like terms: 49x + 16x = 65x
x(28 + 65x + 28x2) = 0
(28 * x + 65x * x + 28x2 * x) = 0
(28x + 65x2 + 28x3) = 0

Solving
28x + 65x2 + 28x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(28 + 65x + 28x2) = 0

Factor a trinomial.
x((7 + 4x)(4 + 7x)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + 4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x = 0 + -7
4x = 0 + -7

Combine like terms: 0 + -7 = -7
4x = -7

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75

Subproblem 3
Set the factor '(4 + 7x)' equal to zero and attempt to solve:

Simplifying
4 + 7x = 0

Solving
4 + 7x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + 7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7x = 0 + -4
7x = 0 + -4

Combine like terms: 0 + -4 = -4
7x = -4

Divide each side by '7'.
x = -0.5714285714

Simplifying
x = -0.5714285714
Solution
x = {0, -1.75, -0.5714285714}

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